Abstract
The basic concepts allowing to define the different states of a dynamical system are illustrated through the behaviour of the Rayleigh-Bénard convection in confined geometry. The interest of the Poincaré sections of the phase space is pointed out in parallel with that of the iterated maps. Finally one shows how the deterministic chaos can be understood, thanks to the concepts of strange attractor.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
L.D. Landau and E.M. Lifshitz “Fluid Mechanics”, Pergamon Press, London 1959.
D. Ruelle and F. Takens, Comm. Math. Phys. 20, 167 (1971).
P. Bergé and M. Dubois “Systems far from Equilibrium” Sitges 1980, Pringer-Verlag ed. by L. Garrido, p. 381.
P. Bergé “chaos and order in nature” Schloss Elman 1981, Springer-Verlag ed. by H. Haken p.14.
P. Bergé and M. Dubois, J. Physique Lettres 40, L505 (1979).
M. Dubois and P. Bergé, Phys. Letters A76, 53 (1980)
M. Dubois, this volume and M. Dubois, P. Bergé and V. Croquette, Comptes Rendus Acad. Sci Paris, Sept. 1981.
E. Lorenz, J. Atmos. Sci 20, 130 (1963).
P. Collet, J.P. Eckmann “Iterated mans on the interval as dynamical systems” P. Ph. ed. A. Jaffe, D. Ruelle, Birkhaüser 1980.
M.G. Velarde in “Non Linear Phenomena at Phase Transitions and Instabilities” NATO Advanced Study Institute, Norway (1981).
M. Dubois in “Symmetries and Broken Symmetries in Condensed Matter Physics” ed. by N. Boccara (IDSET Paris) 1981.
M. Dubois and P. Bergé, J. Physique 42, 167 (1981).
P. Bergé, M. Dubois and V. Croquette “Convective Transport and Instability Phenomena” Euromech 138, Karlsrule 1981 ed. by H. Oertel and J. Zferep.
M. Renon, Commun. Math. Phys. 50, 69–77 (1976).
O.E. Rossler, Phys. Letters A57, 397 (1976).
P. Manneville and Y. Pomeau, Phys. Letters 75A, 1 (1979).
P. Bergé, M. Dubois, P. Manneville and Y. Pomeau, J. Physique Lettres 41, L341 (1980).
M.J. Feigenbaum, Phys. Letters 74A, 375 (1979).
J. Maurer and A. Libchaber, J. Physique Lettres 41, L515 (1980).
M. Giglio, S. Musaggi and U. Perini, to be published.
R. Shaw, Z. Naturforsch 36a, 80 (1981).
A. Arneodo, P. Coullet and C. Tresser, Phys. Letters 79A, 259 (1980).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
Bergé, P. (1982). Some topics about the transition to turbulence. In: Casas-Vázquez, J., Lebon, G. (eds) Stability of Thermodynamics Systems. Lecture Notes in Physics, vol 164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11581-1_5
Download citation
DOI: https://doi.org/10.1007/3-540-11581-1_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11581-6
Online ISBN: 978-3-540-39328-3
eBook Packages: Springer Book Archive